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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH. Chapter 15.1 Heteroscedasticity. Heteroscedasticity. Assumptions of a normal regression model: The disturbances are independent random variables The standard deviations of all disturbances are equal:

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AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

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  1. AAEC 4302ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH Chapter 15.1 Heteroscedasticity

  2. Heteroscedasticity • Assumptions of a normal regression model: • The disturbances are independent random variables • The standard deviations of all disturbances are equal: σ(ui) = σu for all i • Heteroscedasticity occurs when the error term (and thus the dependent variable Y) does not have a constant variance across observations: σ(ui) = σi

  3. Heteroscedasticity

  4. Heteroscedasticity

  5. Heteroscedasticity • The OLS parameter estimators are still unbiased, but OLS standard errors are incorrect • Also, the OLS parameter estimators are no longer the most efficient (i.e. minimum variance), even if the error term is normally distributed

  6. Heteroscedasticity • SAVINGS=-1.062+0.295INCOME (0.851) (0.075) R2=0.137 [1.233] [0.152] Original standard error (t*=3.94) Revised standard error (t*=1.94)

  7. Heteroscedasticity Detection Examine the residuals σ(ui) = σXi • White Test • Breusch-Pagan Test • Park Test • Glejser Test

  8. Heteroscedasticity White test Auxiliary regression H0: σ(ui) = σu - no heteroscedasticity H1: σ(ui) = σi H0 is rejected when nR2 is large

  9. Heteroscedasticity Estimation Respecify the original model in such a way that resulting disturbances are homoscedastic

  10. Heteroscedasticity (0.222) (0.044) SAVINGSi = 0.228 + 0.197 INCOMEi (0.222) (0.044) • GLS (Generalized Least Squares) • Also known as weighted least squares

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